We prove that the number of maximal points in a random sample taken uniformly and independently from a convex polygon is asymptotically normal in the sense of convergence in distribution. Many newâ€¦ (More)

Let X = {x1,x2, . . . ,xn} be a set of independent and identically distributed (iid) random vectors in Rd. A point xi = (xi1, . . . , xid) is said to be dominated by xj if xik < xjk for all k = 1, .â€¦ (More)

We establish the asymptotic normality of the number of upper records in a sequence of iid geometric random variables. Large deviations and local limit theorems as well as approximation theorems forâ€¦ (More)

An asymptotic expression for the expected area of the union of n random rectangles is derived by Mellin transforms, where their two diagonal corners are independently and uniformly distributed overâ€¦ (More)